The trajectory of a MeV proton in a resist material is dependent on the interaction with both the atomic electrons and nuclei in the material. For most of its path, the probability that a proton interacts with an electron is a few orders of magnitude larger than for nuclear scattering and, as a first approximation, nuclear collisions have little effect on the trajectories. Because of the high mismatch in mass between the proton and the material’s electrons (mp/me ≈ 1800), proton collisions with electrons do not result in any significant deviation in the trajectory of a proton from a straight-line path. Further, because of the momentum mismatch, the energy transfer in each proton/electron collision is small and, consequently, many thousands of collisions will occur before a proton comes to rest. The primary interaction of high-energy protons (e.g. 500 keV – 3 MeV) is, therefore, that of deep penetration into the material with a minimal amount of surface disruption. In addition, diffraction effects are not an issue (the wavelength of a 100 keV proton is around 10-4 nm).
The interaction between a proton beam and matter can be summarized as follows:

(i) The proton beam travels in a straight line apart from a small amount of end-of-range broadening (where nuclear collisions become more prominent). This offers a considerable advantage over e-beam writing for fabricating high aspect ratio three dimensional structures, since a finely focused electron beam spreads rapidly as it enters the resist material.

(ii) The exposure as the protons penetrate the material is relatively constant (apart from a ten-fold increase at the end of range). This feature offers an advantage over EUV or X-ray lithographies, which exhibit an exponential reduction in dose with depth.

(iii) The penetration depth of the proton beam is well defined and can be varied by changing the proton beam energy. This is a unique characteristic that allows multilevel structures to be formed in one layer of resist.
(iv) Lithography with protons also offers a virtual absence of high energy secondary electrons that could otherwise give rise to unwanted exposure of the resist (proximity effects). In e-beam writing, for example, a small but significant fraction of secondary electrons are generated with energies that can contribute to the proximity effect in the micron range. Proton trajectories and energy loss profiles can be accurately simulated by means of Monte Carlo calculations, for example using the computer code SRIM [1], and e-beam writing can be simulated using the CASINO code [2]. A comparison between p-beam writing, FIB, and e-beam writing is shown in Fig. 1. Recent Monte Carlo calculations using the Hansen- Kobach-Stolterfoht model for proton-induced secondary electron emission [3] indicate the superior nature of p-beam over e-beam writing with respect to the extent of proximity effects and penetration profiles. The simulations using the δ-simulator computer program show that the use of protons for lithography result in more confined energy density profiles along the proton beam trajectory (Fig. 2). From Fig. 2 it can also be observed that the energy distribution profiles from the proton beam trajectory over the first 2 μm of penetration into the resist is essentially contained within a 10 nm diameter, an improvement of several orders of magnitude compared with electrons.

Figure 1. Comparison between p-beam writing, FIB (focused ion beam technology) and e-beam writing. This figure shows schematically the difference between the three techniques. The p-beam and e-beam images were simulated using SRIM [1] and CASINO [2] software packages respectively.